The Weisfeiler-Lehman Method and Graph Isomorphism Testing

Properties of the `$k$-equivalent' graph families constructed in Cai, F\"{u}rer and Immerman, and Evdokimov and Ponomarenko are analysed relative the the recursive $k$-dim WL method. An extension to the recursive $k$-dim WL method is presented that is shown to efficiently characterise all such types of `counterexample' graphs, under certain assumptions. These assumptions are shown to hold in all known cases.